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Appendix VI.

I2, the value of which is required.    The distance apart of these
axes is #, so by Euclid II. 13

And I2 = 2 m-f* = 2

But, having regard to sign, % m-d = zero,

Also, S*«-£2 = I-L

And, S?//-#2 = whole area x #-

.*. 1 2 = Ij -f (area x #'2)

We may now find the 2nd moment of any beam section that

CAST   //?o/v

of Rje£jusJjcuvc&.   Jfyq. 957.

can be cut up into a number of regular figures whose 2nd mo-
ments are obtainable by well-known formulae, the total value
being the addition of the moments of the parts round the neutral

Two examples have been given in Fig. 957. Taking the
cast-iron beam, the neutral axis is found by moments round H,
as at top of p. 432.

12   X  O     =     O

7i x 4$ = 33*5
IF x 3i =   4'24
3l x 8i = 3°*6

Total moments = 68-34          Total area